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GATE BT 2021 | Question: 44
The determinant of matrix $A = \begin{pmatrix} 1 & 1& 1 & 1 \\ -1 & 1 & 1 & 1 \\ -1 & -1 & 1 & 1 \\ 1 & 1 & 1 & 3 \end{pmatrix}$ is __________.

go_editor asked in Linear Algebra Mar 1, 2021

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2

GATE2020: 23
The largest eigenvalue of the matrix $\begin{bmatrix} 4 &1 \\ -2& 1 \end{bmatrix}$ is ______________.

soujanyareddy13 asked in Linear Algebra Nov 3, 2020

by soujanyareddy13

2.7k points

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3

GATE2020: GA: 9
For a matrix $M=[m_{ij}]; \: i,j=1,2,3,4$, the diagonal elements are all zero and $m_{ij}=-m_{ji}$. The minimum number of elements required to fully specify the matrix is ________ $0$ $6$ $12$ $16$

soujanyareddy13 asked in Quantitative Aptitude Nov 3, 2020

by soujanyareddy13

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4

GATE2019: 20
Matrix $A=\begin{bmatrix} 0&6 \\ p&0 \end{bmatrix}$ will be skew-symmetric when $p$= ____.

soujanyareddy13 asked in Linear Algebra Nov 3, 2020

by soujanyareddy13

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5

GATE2016-23
The positive Eigen value of the following matrix is __________. $\begin{bmatrix} 2 & 1 \\ 5 & -2 \end{bmatrix}$

Milicevic3306 asked in Linear Algebra Mar 26, 2018

by Milicevic3306

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6

GATE2016-54
The value of determinant $A$ given below is ________. $A = \begin{pmatrix} 5 & 16 & 81 \\ 0 & 2 & 2 \\ 0 & 0 & 16 \end{pmatrix}$

Milicevic3306 asked in Linear Algebra Mar 26, 2018

by Milicevic3306

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7

GATE2017-37
The value of $c$ for which the following system of linear equations has an infinite number of solutions is ________ $\begin{bmatrix}1 & 2 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} c \\ 4 \end{bmatrix}$

Milicevic3306 asked in Linear Algebra Mar 26, 2018

by Milicevic3306

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8

GATE2015-39
What are the eigenvalues of the following matrix? $\begin{bmatrix} 1 & 1 \\ -2 & 4 \end{bmatrix}$ $2$ and $3$ $-2$ and $3$ $2$ and $-3$ $-2$ and $-3$

Milicevic3306 asked in Linear Algebra Mar 26, 2018

by Milicevic3306

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9

GATE2015-52
If $A = \begin{bmatrix} 4 & 2 \\ 1 & 3 \end{bmatrix}$, then $A^2+3A$ will be $\begin{bmatrix} 30 & 20 \\ 10 & 20 \end{bmatrix} \\$ $\begin{bmatrix} 28 & 10 \\ 4 & 18 \end{bmatrix} \\$ $\begin{bmatrix} 31 & 13 \\ 7 & 21 \end{bmatrix} \\$ $\begin{bmatrix} 20 & 10 \\ 5 & 15 \end{bmatrix}$

Milicevic3306 asked in Linear Algebra Mar 26, 2018

by Milicevic3306

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10

GATE2014-1
The eigenvalues of A =$\begin{bmatrix} 1&-4\\2 & -3 \end{bmatrix} $are $2\underline{+}i$ $-1, -2$ $-1\underline{+}2i$ non-existent

Milicevic3306 asked in Linear Algebra Mar 26, 2018

by Milicevic3306

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11

GATE2013-40
The solution of the following set of equations is $x+2y+3z=20$ $7x+3y+z=13$ $x+6y+2z=0$ $x=-2, y=2, z=8$ $x=2, y=-3, z=8$ $x=2, y=3, z=-8$ $x=8, y=2, z=-3$

Milicevic3306 asked in Linear Algebra Mar 26, 2018

by Milicevic3306

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12

GATE2013-20
One of the eigcn values of $P=\begin{bmatrix}10 & -4 \\ 18 & -12\end{bmatrix}$ is $2$ $4$ $6$ $8$

Milicevic3306 asked in Linear Algebra Mar 26, 2018

by Milicevic3306

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13

GATE2013-17
If $P=\begin{bmatrix}1&1\\2&2\end{bmatrix}, Q=\begin{bmatrix}2&1\\2&2\end{bmatrix}$ and $R=\begin{bmatrix}3&0\\1&3\end{bmatrix}$, which one of the following statements is $TRUE$? $PQ=PR$ $QR= RP$ $OP=RP$ $PO= OR$

Milicevic3306 asked in Linear Algebra Mar 26, 2018

by Milicevic3306

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14

GATE2012-32
What is the rank of the following matrix? $\begin{bmatrix}5 & 3 & -1\\ 6 & 2 & -4 \\14 & 10 & 0 \end{bmatrix}$ $0$ $1$ $2$ $3$

Milicevic3306 asked in Linear Algebra Mar 25, 2018

by Milicevic3306

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15

GATE2018-21
The determinant of the matrix $\begin{pmatrix} 4 & -6 \\ -3 & 2 \end{pmatrix}$ is _________

gatecse asked in Linear Algebra Feb 20, 2018

1.4k points

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